一类非线性Lyness差分方程的定性分析  

Investigation of the stability of a sort of nonlinear Lyness difference equations

作　　者：崔月娥[1] 张安雨 冯学文[1] 吴开谡[1] 

机构地区：[1]北京化工大学理学院,北京100029

出　　处：《北京化工大学学报（自然科学版）》2013年第B12期95-99,共5页Journal of Beijing University of Chemical Technology(Natural Science Edition)

基　　金：大学生科技创新基金(pt2012062)

摘　　要：研究了一类非线性二阶Lyness差分方程,利用解的不变区间的技巧,证明了解的全局渐近稳定性。将证明所得结论推广到k阶Lyness差分方程上,进一步讨论了k阶Lyness差分方程解的全局渐进稳定性,并给出了两个具体的数值算例。Abstract：The stability of solutions of a sort of non-linear second order Lyness difference equations was investigated in this paper.Using the invariant interval technique,we proved the global asymptotic stability of the solution.Then,the conclusion for the 2-order Lyness difference equation was generalized to k-order Lyness difference equation.Furthermore,we got the global asymptotic stability of the solution of k-order Lyness equation.In the end,two numerical experimentations were carried out.

关 键 词：Lyness差分方程 平衡点 全局渐近稳定 

分 类 号：O175.7[理学—数学] O175.12[理学—基础数学]